ALBANY—In signing a sweeping new set of gun laws Tuesday a month after the Newtown, Conn., school shooting, Gov. Andrew Cuomo tackled an issue the Democratic Party had avoided for more than a decade and put himself in an unusual spot as an object of Republican fury.

Democrats hailed Mr. Cuomo's aggressive gun-control push, citing it as an example of a muscular brand of politics that the governor has made his signature in two years in office. He has bent a Legislature partially controlled by Republicans to his will on other liberal issues, such as legalizing gay marriage and solidifying higher tax rates for the wealthy.

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But Mr. Cuomo's efforts on firearms, coming so soon after a national tragedy and on an issue that Democrats had long ago ceded to the GOP, reignited speculation that he would seek the presidency in 2016 and may have positioned him more favorably with liberal primary voters.

"You've seen him play offense, in a way Democrats typically have not done on the gun-control issue," said Chris Lehane, a Democratic political strategist who has worked for former President Bill Clinton and Vice President Al Gore. "He's a no-huddle governor: He scores points before the other players can even get off the line."

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New York's new gun laws represented a more overtly partisan victory for Mr. Cuomo than his previous achievements. No Republican leaders joined him at the bill signing in the Capitol's ornate Red Room. And for the first time in the governor's tenure, he endured sustained, sometimes furious criticism from GOP lawmakers who said the laws were rushed through.

"Why are we being bullied into voting on this bill?" asked Assemblyman Steve Katz, a Republican who represents parts of Westchester and Putnam counties. Sen. Greg Ball, a Republican from Putnam County north of New York City, said: "The only life that may have been helped by this bill is the political life of Andrew Cuomo on the national stage."

Mr. Lehane said the governor's gun-control efforts would play well with Democratic primary and general election voters. But Dave Carney, a New Hampshire Republican strategist who worked for former President George H.W. Bush, said Mr. Cuomo may have overdone it for moderates. "He reached a bridge too far and too quick," said Mr. Carney.

A savvy, sometimes cautious politician, Mr. Cuomo had cultivated close ties with Albany's Republicans, especially in the Senate where the GOP has traditionally held power. But Republicans lost their majority this year and share power with a group of breakaway Democrats, allowing Mr. Cuomo more room to move to the left.

Mr. Cuomo, whose approval ratings have polled above 70% since superstorm Sandy, characterized the gun debate as a battle he was happy to join. "We are fighting back," he said. "We can strike back and we can defend ourselves, but we're going to do it intelligently."

Mr. Cuomo was, according to people involved with negotiations, eager to be the nation's first governor to sign new gun laws after the Sandy Hook Elementary School shooting in neighboring Connecticut. The accord also put him in front of President Barack Obama, who is set to announce his gun-control initiatives on Wednesday.

A senior Cuomo administration official said the governor had long supported gun control and seized the opportunity after the Newtown shootings provided popular support for new laws. Mr. Cuomo believes he can move the Legislature on almost any issue that has popular support, the official said.

The last major Democratic gun-control initiative came under Mr. Clinton—Mr. Cuomo's former boss—in 1993, with the passage of a federal ban on some military-style rifles. That statute has since lapsed.

Mr. Cuomo's style stands in stark contrast to his counterpart and fellow Democrat in Connecticut, Gov. Dannel Malloy, who is weighing new firearms restrictions and an overhaul of the mental-health system. Mr. Malloy congratulated Mr. Cuomo on Tuesday, but said he would take a more deliberative approach.

"Given what our state has gone through, and given the expressed desire of parents at Sandy Hook specifically to be involved in the process, I'm not envious of how rapidly they are moving," Mr. Malloy said. "We are in a different situation where it's important that we give an opportunity for multiple voices to be heard and then act."

The breadth of the New York legislation impressed gun-control advocates and dismayed its opponents. The new laws classify more semiautomatic rifles as so-called assault weapons, requires many gun owners to renew their licenses every five years, increases the regularity of background checks and makes it illegal to own ammunition magazines with more than seven rounds. It also included a mental-health component, expanding a law that requires some seriously mentally ill people to get treatment and requiring psychiatrists and other providers to report patients who may be dangers to themselves or others.

Some gun-control advocates said the legislation gave New York the nation's most stringent firearms laws. "He didn't pull back at all and end up with a weak bill," said Richard Aborn, president of the Citizens' Crime Commission, a nonprofit criminal-justice policy group.

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